9y^2+2+16=-24y

Solution for 9y^2+2+16=-24y equation:

Simplifying
9y2 + 2 + 16 = -24y

Reorder the terms:
2 + 16 + 9y2 = -24y

Combine like terms: 2 + 16 = 18
18 + 9y2 = -24y

Solving
18 + 9y2 = -24y

Solving for variable 'y'.

Reorder the terms:
18 + 24y + 9y2 = -24y + 24y

Combine like terms: -24y + 24y = 0
18 + 24y + 9y2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(6 + 8y + 3y2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(6 + 8y + 3y2)' equal to zero and attempt to solve:

Simplifying
6 + 8y + 3y2 = 0

Solving
6 + 8y + 3y2 = 0

Begin completing the square.  Divide all terms by
3 the coefficient of the squared term: 

Divide each side by '3'.
2 + 2.666666667y + y2 = 0

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + 2.666666667y + -2 + y2 = 0 + -2

Reorder the terms:
2 + -2 + 2.666666667y + y2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 2.666666667y + y2 = 0 + -2
2.666666667y + y2 = 0 + -2

Combine like terms: 0 + -2 = -2
2.666666667y + y2 = -2

The y term is 2.666666667y.  Take half its coefficient (1.333333334).
Square it (1.777777780) and add it to both sides.

Add '1.777777780' to each side of the equation.
2.666666667y + 1.777777780 + y2 = -2 + 1.777777780

Reorder the terms:
1.777777780 + 2.666666667y + y2 = -2 + 1.777777780

Combine like terms: -2 + 1.777777780 = -0.22222222
1.777777780 + 2.666666667y + y2 = -0.22222222

Factor a perfect square on the left side:
(y + 1.333333334)(y + 1.333333334) = -0.22222222

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.